Revealing mistake: While fighting Clouseau, Cato sticks a wooden pole through the screen of a television. The screen is made of paper. (00:17:30)
Continuity mistake: At the start of the fight in the club, the stain on Clouseau's jacket (from the accident with the parrot) is visible. Partway through the fight it has faded significantly. By the end of the fight it has gone. (00:45:00)
Revealing mistake: When Clouseau answers the phone he shuffles his right foot slightly so that it isn't directly over the spot that Dreyfus drills through a few seconds later. (00:19:45)
Continuity mistake: The President of the US is watching football on channel 1. Dreyfus interrupts the broadcast and an aide flips through the channels to discover that Dreyfus is on all of them - the TV ends up on channel 9. Throughout the rest of the scene, the TV switches back and forth between channels 1 and 9 without human intervention. (00:50:00)
Continuity mistake: After Dreyfus' pirate broadcast we are shown a black and white picture 'taken by a journalist during the broadcast'. The photograph is very unlike any image of Dreyfus' face in his telecast.
Continuity mistake: In the beginning, when Clouseau walks to the door of his apartment, there's a big pile of sugar in the elevator. This pile disappears during his silly dance, but returns when he tears his pants later.
Continuity mistake: When Clouseau, Cato and Olga fall into the river at the end of the film there are two shots of the fall (one from above, one from below). The two shots are different - the people are in different places and there are different amounts of debris and bedding. (01:41:20)
Continuity mistake: When Dreyfus makes the first hole in the ceiling to spy on Clouseau, the latter spills sugar on that spot of the floor. Yet when we look through the telescope, the floor right in front of it has no sugar on it.
Continuity mistake: Inspector Closeau's large rectangular parcel - leaning against the table - changes position while he is opening the door to his flat. (00:13:45)
Revealing mistake: When Clouseau is on the parallel bars, note the switch as he jumps and turns from Peter Sellers to stuntman, then note again as the stuntman falls down the stairs; the stuntman finishes falling behind the right hand side of the settee, and up pops Peter Sellers on the left hand side of the settee giving the apparant impression he has just fallen down the stairs himself.
Continuity mistake: When Clouseau hits Cato with a nunchaku, Cato is holding his pole in the middle. In the next shot, his hands have moved to the bottom of the pole.
Revealing mistake: When Clouseau yanks a man's tooth out, you can still see it; it's just blackened to appear missing.
Revealing mistake: When Clouseau pulls out Dreyfus' tooth there is no blood. (01:31:00)
Continuity mistake: In the hallway, Clouseau has spaghetti and a french loaf sticking up out of his shopping bag. When he enters his flat, the loaf has vanished. (00:14:05)
Revealing mistake: Throughout the whole scene when Clouseau is disguised as a hunchback and is floating out the window, you can see wires.
Revealing mistake: When Clouseau is floating out of his apartment in his costume, in several shots you can see the shadows of the chimney behind him in the sky, indicating this was shot in a studio.
Revealing mistake: When Clouseau strikes Cato on the back of his head with the shinai it's actually just hitting the doorframe to his right with Cato flipping forward on cue.
Continuity mistake: Clouseau's clothes go back and forth from being wet to dry during his numerous and failed attempts to get into Dreyfus' castle and falling into the moat instead.
Continuity mistake: When Dreyfus goes crazy again he's completely soaked, When he's chasing Clouseau he's suddenly dry.
Continuity mistake: At the very end of the film when the bed crashes through the wall, Olga has disappeared from the very first outside shot. She is then back to the left of Cato in the next shot. This was likely done because she was completely nude and the audience would've got a good look at her.
Answer: Just Invisible. Besides the fact that his eyeball and eyelid remain intact and in the same position, he returns in a full, visible form (possibly in a film logic borrowed from Looney Tunes cartoons) in the next Panther film.